Kostant asked the following question: Let g be a simple Lie algebra over the complex
numbers. Let λ be a dominant integral weight. Then, V (λ) is a component of V (ρ)⊗ V (ρ) if …

For a simple Lie algebra g of type A n, B n, C n or D n, we give a characterization of the set of
dominant integral weights λ such that for any rational point μ in the fundamental Weyl …

Let g be a complex simple Lie algebra and let g 0 be the sub-algebra fixed by a diagram
automorphism of g. Let G be the complex, simply-connected, simple algebraic group with Lie …

We present some results about the irreducible representations appearing in the exterior
algebra Λ g, where g is a simple Lie algebra over C. For Lie algebras of type B, C or D we …

In this paper, using crystal theory we prove the existence of a new family of irreducible
components appearing in the tensor product of two irreducible integrable highest weight …

For a complex simple Lie algebra $\mathfrak {g} $ or rank $ r $, let $\rho $ be the half sum of
positive roots and $ P (2\rho)\subset\mathbb {R}^ r $ be the convex hull of all dominant …

Let $\mathfrak g $ be a simple Lie algebra with Cartan subalgebra $\mathfrak {h} $ and Weyl
group $ W $. We build up a graded isomorphism $\bigl (\bigwedge\mathfrak …

Kostant asked the following question: Let g be a simple Lie algebra over the complex
numbers. Let λ be a dominant integral weight. Then, V (λ) is a component of V (ρ)⊗ V (ρ) if …

Reeder’s Conjecture for Lie Algebras of type C Page 1 Universit`a di Firenze, Universit`a di
Perugia, IndAM consorziate nel CIAFM DOTTORATO DI RICERCA In MATEMATICA …